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"If one of our clients requests a quote for materials, we have the responsibility to do so," the company said in a statement. "But this does not imply that Cemex will participate in the project."

If Cemex does get involved, that could test Trump's promise to "buy American, hire American."

That's because Cemex has a huge presence in the U.S., with offices in Houston and New York. Its cement is being used to build the largest building in San Francisco, the Salesforce Tower, and an 83-story skyscraper in Miami.

The U.S. is the company's biggest market, accounting for 28 percent of its sales. About 20 percent of its revenues come from Mexico and 22 percent from northern Europe.

Cemex say it has roughly 10,000 employees in both Mexico and the United States. It has 43,000 employees worldwide.

Costs, timeline of wall unclear

The Trump administration has provided few details about the wall. But the president did say last week that construction of the wall is "going to start soon" and it's "way ahead of schedule."

Trump is adamant that Mexico will pay for the wall, but the Mexican government has repeatedly said it will not pay for the wall under any circumstance. During his campaign, Trump threatened to restrict or tax cash sent that's sent home to Mexico by Mexican workers in the U.S. But he hasn't commented on that since taking office.

It's not clear how much the wall will cost. Reuters reported in February, citing an internal Department of Homeland Security report, that the wall would cost about $21 billion, far higher than Trump's recent estimate of $12 billion.